Isolated planar mesogyroscope

ABSTRACT

An inertial sensor includes a mesoscaled disc resonator comprised of micro-machined substantially thermally non-conductive wafer with low coefficient of thermal expansion for sensing substantially in-plane vibration, a rigid support coupled to the resonator at a central mounting point of the resonator, at least one excitation electrode within an interior of the resonator to excite internal in-plane vibration of the resonator, and at least one sensing electrode within the interior of the resonator for sensing the internal in-plane vibration of the resonator. The inertial sensor is fabricated by etching a baseplate, bonding the substantially thermally non-conductive wafer to the etched baseplate, through-etching the wafer using deep reactive ion etching to form the resonator, depositing a thin conductive film on the through-etched wafer. The substantially thermally non-conductive wafer may comprise a silicon dioxide glass wafer, which is a silica glass wafer or a borosilicate glass wafer, or a silicon-germanium wafer.

CROSS-REFERENCE TO RELATED APPLICATIONS

This divisional application claims the benefit under 35 U.S.C. §120ofthe following co-pending U.S. patent application:

U.S. patent application Ser. No. 11/103,899, filed Apr. 12, 2005, byChalloner et al., entitled “ISOLATED PLANAR MESOGYROSCOPE,” which claimsthe benefit of U.S. Provisional Patent Application Ser. No. 60/561,323,filed Apr. 12, 2004, by Challoner et al., entitled “MESOGYROSCOPE,” andwhich is a continuation-in-part of both U.S. Utility patent applicationSer. No. 10/639,134, filed Aug. 12, 2003, by Shcheglov et al., entitled“CYLINDER GYROSCOPE WITH INTEGRAL SENSING AND ACTUATION” and U.S.Utility patent application Ser. No. 10/639,135, filed Aug. 12, 2003, byShcheglov and et al., entitled “CYLINDER GYROSCOPE WITH INTEGRAL SENSINGAND ACTUATION.”

This application is related to the following patents:

U.S. Pat. No. 6,629,460, issued Oct. 7, 2003 to A. Dorian Challoner,entitled “ISOLATED RESONATOR GYROSCOPE,”

U.S. Pat. No. 6,698,287, issued Mar. 2, 2004, to Randall L. Kubena,Richard Joyce, Robert T. M'Closkey and A. Dorian Challoner, entitled“MICROGYRO TUNING USING FOCUSED ION BEAMS,”

U.S. Pat. No. 6,915,215, issued Jul. 5, 2005 to Robert M'Closkey, A.Dorian Challoner, Eugene Grayver and Ken J. Hayworth, entitled“INTEGRATED LOW POWER DIGITAL GYRO CONTROL ELECTRONICS,”

U.S. Pat. No. 6,955,084, issued Oct. 18, 2005 to A. Dorian Challoner andKirill V. Shcheglov, entitled “ISOLATED RESONATOR GYROSCOPE WITH COMPACTFLEXURES,”

U.S. Pat. No. 6,990,863, issued Jan. 31, 2006 to A. Dorian Challoner andKirill V. Shcheglov, entitled “ISOLATED RESONATOR GYROSCOPE WITHISOLATION TRIMMING USING A SECONDARY ELEMENT,”

U.S. Pat. No.7,017,410, issued Mar. 28, 2006 to A. Dorian Challoner andKirill V. Shcheglov, entitled “ISOLATED RESONATOR GYROSCOPE WITH A DRIVEAND SENSE FRAME,”

U.S. Pat. No. 7,100,444, issued Sep. 5, 2006 to A. Dorian Challoner,entitled “ISOLATED RESONATOR GYROSCOPE,”

which patents are incorporated by reference herein.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to gyroscopes, and in particular tomesoscale disc resonator gyroscopes or isolated planar mesogyroscopesand their manufacture.

2. Description of the Related Art

Mechanical gyroscopes are used to determine direction of a movingplatform based upon the sensed inertial reaction of an internally movingproof mass. A typical electromechanical gyroscope comprises a suspendedproof mass, gyroscope case, pickoffs, forcers and readout electronics.The inertial proof mass is internally suspended from the gyroscope casethat is rigidly mounted to the platform and communicates the inertialmotion of the platform while otherwise isolating the proof mass fromexternal disturbances. The pickoffs that sense the internal motion ofthe proof mass, the forcers that maintain or adjust this motion and thereadout electronics that must be in close proximity to the proof massare internally mounted to the case, which also provides the electricalfeedthrough connections to the platform electronics and power supply.The case also provides a standard mechanical interface to attach andalign the gyroscope with the vehicle platform. In various forms,gyroscopes are often employed as a critical sensor for vehicles such asaircraft and spacecraft. They are generally useful for navigation orwhenever it is necessary to autonomously determine the orientation of afree object.

Older conventional mechanical gyroscopes were very heavy mechanisms bycurrent standards, employing relatively large spinning masses. A numberof recent technologies have brought new forms of gyroscopes, includingoptical gyroscopes, such as laser gyroscopes and fiberoptic gyroscopes,as well as mechanical vibratory gyroscopes.

Spacecraft generally depend on inertial rate sensing equipment tosupplement attitude control. Currently, this is often performed withexpensive conventional spinning mass gyros (e.g., a Kearfott inertialreference unit) or conventionally-machined vibratory gyroscopes (e.g., aNorthrup Grumman hemispherical resonator gyroscope inertial referenceunit). However, both of these are very expensive, large and heavy.

In addition, although some prior smaller, micromachined symmetricvibratory gyroscopes have been produced, their vibratory momentum istransferred through the case directly to the vehicle platform, so theyare not isolated. This transfer or coupling admits external disturbancesand energy loss indistinguishable from inertial rate input and henceleads to sensing errors and drift. One example of such a vibratorygyroscope may be found in U.S. Pat. No. 5,894,090, which is incorporatedby reference herein, and which describes a symmetric cloverleafvibratory gyroscope design. Other planar tuning fork gyroscopes mayachieve a degree of isolation of the vibration from the baseplate;however, these gyroscopes lack the vibrational symmetry desirable fortuned operation.

In addition, shell mode gyroscopes, such as the hemispherical resonatorgyroscope and the vibrating thin ring gyroscope, are known to have somedesirable isolation and vibrational symmetry attributes. However, thesedesigns are not suitable for or have significant limitations with thinplanar microfabrication. The hemispherical resonator employs theextensive cylindrical sides of the hemisphere for sensitiveelectrostatic sensors and effective actuators. However, its high aspectratio and three-dimensional (3D) curved geometry is unsuitable forinexpensive thin planar microfabrication. The thin ring gyroscope (e.g.,U.S. Pat. No. 6,282,958, which is incorporated by reference herein),while suitable for thin planar microfabrication, lacks electrostaticsensors and actuators that take advantage of the extensive planar areaof the device. Furthermore, the symmetry of shell-mode gyroscopes isinherently limited by the average mechanical precision of only the twomachining cuts used to define the inner and outer surface. Moreover, theelectrical baseplate or case for this gyroscope is not of the samematerial as the resonator proof mass so that the alignment of thepickoffs and forcers relative to the resonator proof mass change withtemperature, resulting in gyroscope drift. This drift issue is furthercompounded when the electrical base or case of the gyroscope chip ismounted flat to a platform of dissimilar material, as typical withelectronic chip components.

Vibration isolation using a low-frequency seismic support of the case orof the resonator, internal to the case is also known (e.g., U.S. Pat.No. 6,009,751, which is incorporated by reference herein). However, suchincreased isolation comes at the expense of proportionately heavierseismic mass and/or lower support frequency. Both effects areundesirable for compact tactical inertial measurement unit (IMU)applications because of proof mass misalignment under accelerationconditions.

Furthermore, the scale of previous silicon microgyroscopes (e.g., U.S.Pat. No. 5,894,090, which is incorporated by reference herein) cannot beoptimized for navigation or pointing performance resulting in highernoise and drift than desired. This problem stems from dependence onout-of-plane bending of thin epitaxially grown silicon flexures todefine critical vibration frequencies that are limited to 0.1% thicknessaccuracy. Consequently, device sizes are limited to a few millimeters.Such designs exhibit high drift due to vibrational asymmetry orunbalance and high rate noise due to lower mass which increases thermalmechanical noise and lower capacitance sensor area which increases rateerrors due to sensor electronics noise.

High value commercial or military applications require much higherinertial quality. However, millimeter (mm) scale micromachined devicesare inherently less precise and noisier than centimeter (cm) scaledevices, for the same micromachining error. Scaling up of non-isolatedsilicon microgyroscopes is also problematic because external energylosses will increase with no improvement in resonator Q and no reductionin case-sensitive drift. An isolated cm scale resonator with many ordersof magnitude improvement in 3D manufacturing precision is required forvery low drift and noise pointing or navigation performance.

For high mechanical quality (Q>1,000,000) needed for low drift sensors,thermoelastic damping must be very low. To minimize mechanicalvibrational energy loss through thermal energy dissipation, thegyroscope's elements must vibrate either adiabatically or isothermally.Silicon is highly thermally conductive, and therefore thin elements,e.g., 2.5 microns wide, for isothermal vibration have been commonly usedin MEMS designs, i.e., thermal relaxation time is much shorter than thevibration period. More precisely micromachined thick silicon beams wouldbe impractically thick for very long thermal relaxation times andeffective adiabatic operation.

Fused quartz, PYREX, or silicon-germanium (SiGe) alloy, on the otherhand, is much less thermally conductive, so that practically thick beamscan be used with adiabatic vibration, i.e., thermal relaxation time isvery long relative to the vibration period. At mesoscale, the requiredelement thickness, ˜100 um, is practical and, for the same fixed etchingerror, e.g., 0.1 micron, yields much more precisely symmetricmicromachined devices than at microscale, e.g., <10 um, as well as muchincreased mass and reduced thermal noise and much increased area andhence reduced capacitive sensor noise. Low thermal conductivitymaterials with low thermal expansion coefficient coupling thermal tomechanical energy, e.g., fused quartz, have been discovered to beremarkably ideal for adiabatic vibration with low thermoelastic dampingand feasible to micromachine for a planar mesoscale resonator. Thehigher volume to surface ratio inherent with mesoscale vs. microscaledevices results in the reduced effect of surface related damping onoverall mechanical quality, such as losses at or within any conductivelayer, or losses due to surface roughness. Conventionally machinednavigation grade resonators, such as chrome-plated fused quartzhemispherical or shell gyros, have the optimum noise and driftperformance at large scale, e.g., 30 mm and 3D manufacturing precision;however, such gyros are expensive and difficult to manufacture.

The low thermal conductivity desired for adiabatic operation comes atsome cost, as the materials that have low thermal conductivity also tendto be electrically insulating (with the exception of SiGe, which can bemade sufficiently electrically conductive by bulk doping). This featuremust be dealt with as electrical conductivity is necessary for theelectrostatic driving and sensing of the resonator. In particular, fusedsilica, a material that has the best thermoelastic properties at themesoscale of those commonly available, is also a very good insulator. Toovercome this, a very thin conductive film is deposited onto theresonator and electrode surfaces. This film provides adequateconductivity (low enough resistance so that the electronics do not pickup additional noise and parasitic signals) while not affecting themechanical Q. Preferably, the film is very thin and uniform.

There is a need in the art for a micromachined, Coriolis-sensing,mesogyroscope with thick mesoscale, adiabatically vibrating elements andan electrically conductive resonator for electrostatic sensing,actuation and trimming. Specifically, there is a need for amesogyroscope that has lower cost and higher precision thanone-at-a-time, conventional, 3D machined, mesoscale, Coriolis-sensinggyroscopes, and that has higher mechanical precision and performancethan other micromachined gyroscopes with thin, microscale, isothermallyvibrating elements or micromachined, mesoscale, silicon gyroscopes.There is also a need for a mesogyroscope that also has higherperformance due to its electrically conductive resonator permittinghighly sensitive capacitive or tunneling sensing and capacitiveactuation as compared to micromachined gyroscopes with piezoelectricmaterials or sensing and actuation elements attached. As detailed below,the present invention satisfies all these and other needs.

SUMMARY OF THE INVENTION

The present invention discloses an inertial sensor that includes amesoscaled disc resonator comprised of micromachined substantiallythermally nonconductive material for substantially in-plane solid discvibration with two isolated and degenerate resonator modes for Coriolissensing, a rigid support coupled to the resonator at a central mountingpoint of the resonator, at least one excitation electrode within aninterior of the resonator to excite internal in-plane vibration of theresonator, and at least one sensing electrode within the interior of theresonator for sensing the internal in-plane vibration of the resonator.Typically, the sensor is electrostatically trimmed using other biaselectrodes within the interior of the resonator, so as to compensate allelastic and damping asymmetry resulting from initial micromachining orfinal mechanical trimming with laser or ion beams. The disc resonatorgyroscope sense and actuator electrodes can be arranged to support anycommon form of vibratory gyroscope operation including open loop andclosed loop output, whole angle or free precession, and a novel forcedprecession or inertial wave operation inspired by the high precision andquality enabled by isolated planar mesogyroscopes, and particularly, amesoscale disc resonator mesogyroscope with rich opportunities forinternal electrodes for sensing, actuation and biasing.

The inertial sensor is generally fabricated by etching a baseplate,bonding a substantially thermally non-conductive wafer to the etchedbaseplate, and through-etching the wafer to form a mesoscaled resonator.The baseplate may have electrical lines for contacting the electrodes,or may be just a mechanical support for the resonator and electrodes,with the relevant electrical connections made at a later time by bondinga third wafer to the resonator/baseplate stack. In the latter case, thebaseplate may subsequently be removed using a wet or dry releaseprocess, or may be left in place. The wafer may be a silicon dioxideglass wafer, such as a silica glass wafer or a borosilicate glass wafer,or silicon-germanium, or a fused silica wafer. Ideally all the wafers(the baseplate wafer, the resonator wafer, and the optional third waferwith electrical wiring) should be comprised of the same material (suchas all three are fused silica, or all three are SiGe) to ensure the beststability over temperature and thus maximum gyro performance, or at thevery least be comprised of materials with very similar thermal expansioncoefficients.

BRIEF DESCRIPTION OF THE DRAWINGS

Referring now to the drawings in which like reference numbers representcorresponding parts throughout:

FIG. 1A depicts a top view of an exemplary planar resonator gyroscope ofthe present invention;

FIG. 1B depicts a side view of an exemplary planar resonator gyroscopeof the present invention;

FIG. 1C illustrates a pattern for an exemplary planar resonator of thepresent invention;

FIG. 1D illustrates electrode operation for a first mode of an exemplaryresonator.

FIGS. 2A-2C illustrate masks that can be used in producing an isolatedresonator of the invention;

FIGS. 3A-3C depicts various stages of an exemplary manufacturing processfor the invention;

FIG. 3D shows an exemplary resonator with a quarter cutaway to revealthe embedded electrodes;

FIGS. 3E and 3F illustrate the possible fabrication process flows;

FIG. 3G shows an exemplary gyro in a typical chip-scale packagingassembly;

FIG. 4 is a flowchart of an exemplary method of producing a resonatoraccording to the present invention; and

FIG. 5 illustrates an alternate isolated planar resonator gyroscopeembodiment comprising four masses vibrating in plane.

DETAILED DESCRIPTION

In the following description of the preferred embodiment, reference ismade to the accompanying drawings which form a part hereof, and in whichis shown by way of illustration a specific embodiment in which theinvention may be practiced. It is to be understood that otherembodiments may be utilized and structural changes may be made withoutdeparting from the scope of the present invention.

1.0 Overview

The present invention describes a micromachined, Coriolis-sensing,mesogyroscope with thick mesoscale, adiabatically vibrating elements andan electrically conductive resonator for electrostatic sensing,actuation and trimming. The two-dimensional (2D) micromachined waferfabrication of this mesogyroscope results in lower cost and higherprecision than one-at-a-time, conventional, 3D machined,Coriolis-sensing, mesoscale gyroscopes, and has higher mechanicalprecision and performance than other micromachined gyroscopes with thinmicroscale, isothermally vibrating elements or micromachined mesoscalesilicon gyroscopes. The mesogyroscope of the present invention also hashigher performance due to its electrically conductive resonator,permitting highly sensitive capacitive or tunneling sensing andcapacitive actuation and electrostatic trimming of asymmetry as comparedto micromachined gyroscopes with piezoelectric material or sensing andactuation elements attached.

Generally, embodiments of the invention comprise isolated planarvibratory gyroscopes that employ embedded sensing, actuation andelectrostatic bias trimming providing a planar micromachinedmesogyroscope having desirable axisymmetric resonator with singlecentral nodal support, integral (and distributed) proof mass andflexural suspension and extensive capacitive electrodes with large totalarea. Advantageously, the mesogyroscope is fabricated with low-cost,wafer-level micromachining methods, yet has performance and precisionexceeding that of one at a time, conventionally machined gyroscopes.

Silicon ring resonators (e.g., U.S. Pat. No.6,282,958, which isincorporated by reference herein) do not have large area internalcapacitive sensors, actuators and bias trimming and require flexiblesupport beams. Other quartz hemispherical resonator gyroscopes are threedimensional, so they cannot be micromachined and do not have embeddedelectrodes. Although post mass type resonator gyroscopes (e.g., U.S.Pat. No. 6,629,460, which is incorporated by reference herein) have highangular gain for Coriolis sensing, large area sensing elements and hencesuperior noise performance to other designs, they do not have theoptimized resonator isolation properties of a single central nodalsupport and often employ a discretely assembled post proof mass.Further, integrally made, fully differential embedded electrodes as withthe present invention, desirable for better thermal and vibrationperformance, are not possible with a discrete post proof mass resonatorgyroscope or out of plane gyroscope.

The principal problems with ring gyroscopes are the inherently smallsensor area around a thin ring and the flexibility or interaction of thesupport beams. A three dimensional hemispherical gyroscope has tallersides for large area capacitive sensing, but still requires assembly ofa discrete circumferential electrode cylinder or cup for sensing andexcitation and electrostatic bias trim. A tall cylinder with centralsupport and circumferential electrodes also faces this problem. A shortsolid cylinder or disc with a central support and piezoelectric and/orelectromagnetic wire sensors and actuators, mounted to the top or bottomsurface of the disc solves the problem of non-embedded sensors withsmall area. However, a preferred embodiment of this invention is amultiple slotted disc resonator illustrated in the exemplary embodimentdescribed hereafter.

2.0 Exemplary Planar Resonator Gyroscope Embodiment

FIG. 1A depicts a schematic top view of an isolated resonator for thegyroscope or inertial sensor embodiment of the present invention. Thegyroscope comprises a unique planar resonator 100 which is supported bya rigid central support 106 and designed for in-plane vibration. In theexemplary embodiment, the resonator 100 comprises a disc resonator thatincludes a number of slots, e.g., 116A-116D (generally referenced as116) formed from concentric circumferential segments 104A-104E. Thecircumferential segments 104A-104E are supported by radial segments102A-102E. The overall diameter of the resonator 100 can be varieddepending upon the performance requirements. For example, a 16 mmdiameter resonator 100 can provide relatively high machining precisionand low noise. Further refinement of the resonator 100 can yield aresonator 100 diameter of only 8 mm at significantly reduced cost.

FIG. 1 B depicts a schematic side view of an exemplary isolatedresonator 100 of the present invention assembled into a baseplate 112.The central support 106 supports the resonator 100 on the baseplate 112.At least some of the slots 116 in the resonator 100 provide access forthe embedded electrodes 108A-108D, which are also supported on pillars114 on the baseplate 112. The electrodes 108A-108D form capacitive gaps110A-110H (outward gaps 110A, 110C, 110F and 110H and inward gaps 110B,110D, 110E and 110G) with at least some of the circumferential segments104A-104E of the resonator 100. These electrodes 108A-108D provide forradial excitation of the resonator 100 as well as sensing motion of theresonator 100. To facilitate this each of the electrodes 108A-108D isdivided into multiple separate elements to improve control and sensingof the resonator 100. For example, the annular electrode 108B as showncan be divided into two or more elements, at least one acting across theoutward gap 110C and at least one acting across the inward gap 110D.Vibration is induced in the resonator 100 by separately exciting theelements to produce a biased reaction on the resonator 100 at theelectrode 108B location. Sensing and excitation of either degeneratemode for Coriolis sensing is possible with various internal electrodearrangements. Wider mesoscale resonator 100 beams also offer favorablewide area capacitive sensing and excitation opportunities using thebottom or top beam surfaces with electrodes plated adjacent to the beamson the baseplate 112 under the resonator 100 or on a cap plate situatedabove the resonator 100.

In general, the excitation electrodes 108B, 108C are disposed closer tothe central support 106 (i.e., within inner slots of the resonator 100)than the electrodes 108A, 108D (i.e., within outer slots of theresonator 100) to improve sensing. However, the arrangement anddistribution of the excitation and sensing electrodes 108A-108D can bevaried as desired. Extensive middle electrodes can also be used to biasthe resonator 100 providing complete electrostatic trimming or tuning todegeneracy or for parametric driving with or without trim of dampingasymmetry. Such biasing electrodes typically include multiple separateelements as the excitation and sensing electrodes.

The much improved precision, higher mechanical quality, lower noise andhigher figure of merit inherent in a micro-machined mesogyroscope withrich opportunities for internal sense, control and bias electrodes,inspires off-line or on-line identification of as-machined asymmetry andfull electrostatic elastic trimming to achieve complete tuning or modaldegeneracy to the limits of sensor noise. Measured transfer functionsfrom two independent drive axes to two independent sense axes providesufficient parametric information, such as frequency split and gain todefine the direction of the principal stiffness axes and the stiffnessasymmetry. Voltages are then adjusted or trimmed on selected biaselectrode segments to provide compensating electrostatic stiffnessadjustments along the identified directions and to the degree required.The latter sensitivity is determined empirically or according to asystematic model, such as structural finite element model of theresonator incorporating electrostatic bias forces. In a similar fashion,the damping asymmetry leading to case sensitive gyro drift can beidentified off-line and a conventional output bias compensationalgorithm can be applied to compensate for the effect of the identifieddamping asymmetry vs. location of the vibration pattern. This algorithmtypically employs a polynomial in temperature or resonator frequency todetermine a bias correction. Alternatively, identified damping asymmetrycan be electrostatically compensated by means of the rich bias electrodeopportunities using a trimmed, segmented circumferential parametricdrive at twice resonator frequency. The local amplitude of the driveused to overcome overall resonator damping is trimmed at specificazimuth segments to fully compensate damping asymmetry and hence zeroout case-sensitive gyro drift. In summary, an isolated planarmesogyroscope implemented with the disc resonator gyroscope has inspireda breakthrough in the level and generality of symmetry so that the driftperformance achieved with trimmed vibratory gyroscopes begins toapproach sensor noise limits rather than coarser manufacturing limits.

Parametric drive can also be used to lock the two Coriolis-coupled modesto an external frequency reference. This may be desirable, since atomicvapor-stabilized frequency references can achieve stabilities order ofmagnitude beyond those seen in mechanical resonators. This scheme cansignificantly reduce the noise due to frequency drift.

The precision, high quality and rich internal electrode opportunities ofan isolated planar disc mesogyroscope inspire the conception of thefirst inertial wave based operation of a vibratory gyroscope. In simpleterms, rather than fix the gyroscope vibration pattern in the case aswith conventional open loop or closed loop output operation, or allowthe pattern to freely precess as in conventional whole angle or rateintegrating mode, the vibration pattern is electrostatically precessedin a constantly traveling inertial wave, just as though the case wereundergoing a fixed inertial input rate, Ω₀ and the vibration pattern wasfreely precessing. Fundamental to vibratory gyroscope design is thatthis free precession rate is non-zero in the case and hence observablefor determining inertial rate. Equivalently, the mode of vibration musthave a finite angular gain, k>0 for Coriolis sensing, e.g., is avibrating hemispherical shell resonator, cylindrical shell or ringresonator, in-plane disc resonator or a rocking post but not a rockingplate resonator. Electrostatically forced precession of the resonatorvibration pattern at a high constant rate independent of the input caseinertial rotation rate enables the residual asymmetries to be averagedto zero over one precession cycle in the case. Analogous to closed loopoutput operation at effectively zero precession rate in the case, inwhich the “force to rebalance” is a measure of inertial input rate, ininertial wave operation at constant non-zero precession rate in thecase, the total force to precess is a now a measure of the inertialinput rate, Ω plus the removable constant inertial rate, Ω₀ associatedwith the constantly traveling inertial wave. This eliminates thefundamental problem afflicting conventional vibratory gyroscopes that,in effect, require a non-zero case inertial input rate to precess thevibration pattern and thus cannot distinguish inertial precession fromcase-sensitive drift.

In addition, the forced precession rate or path of the vibration patterncan be non-constant or more generally prescribed or controlled toachieve the best performance possible (e.g., the prescribed precessionrate can be varied or adjusted according closer to the currently sensedrotation rate). Periodic precession patterns may be feasible as well,enabling both drift compensation and dynamic tuning of the resonator oron-line identification of residual asymmetry.

FIG. iC illustrates a pattern 120 for an exemplary disc resonator 100 ofthe present invention. This pattern 120 employs numerous concentricinterleaved circumferential slots 122. Some of the slots, e.g.,122A-122E, are wider to accommodate multiple element electrodes. Forexample, two of the outer rings of wider slots 122A, 122B are for thesensing electrodes and three of the inner rings of wider slots are forthe driving electrodes. The remaining slots 122 can serve toelectrostatically tune the resonator 100 (e.g., lower the frequency)and/or they may be occupied by bias electrodes which are used toactively bias the resonator in operation. The resonator 100 and typicalmodal axes 124 are indicated; operation of the resonator 100 identifiesthem as the pattern 120 is symmetric.

Although the exemplary resonator 100 is shown as a disc, other planargeometries using internal sensing and actuation are also possibleapplying principles of the present invention. In addition, furthermore,the single central support 106 is desirable, providing completeisolation of the resonator 100; however, other mounting configurationsusing one or more additional mounting supports are also possible.

As employed in the resonator 100 described above, a centrally supportedsolid cylinder or disc has two isolated degenerate in-plane radial modessuitable for Coriolis sensing; however, the frequencies are very high(greater than 100 KHz) and the radial capacitance sensing areadiminishes with decreasing cylinder height or disc thickness. Themulti-slotted disc resonator 100, shown in FIGS. 1A and 1B, overcomesthese problems. By etching multiple annular slots through the cylinderor disc, two immediate benefits result: (1) two degenerate modessuitable for Coriolis sensing with low frequency (less than 50 KHz), and(2) large sense, bias and drive capacitance. The low frequency derivesfrom the increased radial compliance provided by the slots. The largesense, bias and drive capacitance is a consequence of the large numberof slots that can be machined into the resonator and populated withelectrodes.

FIG. 1D illustrates electrode operation for a first mode of theresonator 100 of FIG. 1C. The electrodes 124 that operate with aresonator 100 of the pattern 120 are shown in the left image. Fourgroups of electrodes 124 are used, each at a 90° interval around thecircumference of the pattern. The positive excitation elements 126 andnegative excitation elements 128, which are paired elements, are drivento excite the resonator 100. These paired elements 126, 128 share a slotwith the positive elements 126 in the outward position and the negativeelements 128 in the inward position. Note also that as shown some of thepaired elements 126, 128 share a common slot with other distinct pairedelements 126, 128, illustrating that multiple separately operableelectrodes can share a common resonator 100 slot. The sensing electrodesare disposed at a larger radial position and include positive sensingelements 130 and negative sensing elements 132 which together provideoutput regarding motion of the resonator 100.

The electrode segments 134 can be biased for electrostatic trimming tocompensate elastic or mass unbalance in any principal in-plane directionor used for uniform circumferential parametric drive of the resonator attwice resonator frequency to overcome material damping. Fine adjustmentsor trimming of the parametric drive voltage and electrostatic forcesapplied to selected segments can also be used to trim residual dampingasymmetry due to gap non-uniformity or material damping non-uniformity.

A uniform radial spacing between slots 116, 122 can be employed, butother spacing may also be used, provided two isolated, degenerate radialmodes suitable for Coriolis sensing are maintained. In addition, infurther embodiments, some or all of the segments 104A-104E can befurther slotted such that a single beam segment is further divided intoa composite segment including multiple parallel segments. Selective useof such composite segments can be used to adjust the frequency of theresonator 100 Generally, adding slots 116, 122 to form compositecircumferential segments lowers the resonator 100 frequency. The effectof machining errors is also mitigated with multiple slots. Although suchcomposite segments are preferably applied to the circumferentialsegments 104A-1 04E, the technique can also be applied to the radialsegments 102A-102E or other designs with other segments in otherresonator patterns.

Employing the in-plane design described, embodiments of the presentinvention obtain many advantages over other out-of-plane gyroscopes. Forexample, the central support bond carries no vibratory loads,eliminating any friction possibility or anchor loss variability. Inaddition, simultaneous photolithographic machining of the resonator andelectrodes is achieved via the slots. Furthermore, diametral electrodecapacitances can be summed to eliminate vibration rectification andaxial vibration does not change capacitance to a first order. Modalsymmetry is also largely determined by photolithographic symmetry notwafer thickness as with other designs. Isolation and optimization ofsense capacitance (e.g., from the outer slots) and drive capacitance(e.g., from the inner slots) is achieved. Embodiments of the inventionalso achieve a geometric scalable design to smaller or larger diametersand thinner or thicker wafers. In addition, embodiments of the inventioncan be entirely defined by slots of the same width for machininguniformity and symmetry.

As mentioned above, high thermoelastic damping due to vibrationfrequency proximity to thermal relaxation resonance can result in shortresonance decay times and high gyro drift. However, the slot radialspacing can be adjusted to define an optimum beam width and a number ofslots can be additionally etched in between the slots defining theelectrode gaps to further reduce the vibrating beam width.

3.0 Producing an Isolated Planar Resonator Gyroscope

FIGS. 2A-2C illustrate masks that can be used in producing an isolatedresonator of the invention. FIG. 2A illustrates a top view of themulti-slotted disc resonator fabrication pattern 200. The resonatorpattern 200 includes a large central area 202 which is bonded to thecentral support on the baseplate. The embedded electrodes, e.g.,concentric annular electrodes 204A-204F, are defined by the throughetching process that simultaneously defines the structure 206 (radialand circumferential segments) of the resonator. FIG. 2B illustrates atop view of the multi-slotted disc baseplate pattern 208 showing thebonding pads, e.g., electrode bonding pads 210A-210F and the centralsupport bonding pad 212. FIG. 2C illustrates a top view of themulti-slotted disc resonator bonded to the baseplate. To illustrate thealignment, the electrode bonding pads 210A-210F and central supportbonding pad 212 are shown through the electrodes and resonator structure206, respectively. Known manufacturing processes can be employed.

A mesoscaled, e.g., 1 cm, version of the disc resonator gyroscope ismicromachined from a substantially thermally non-conductive material,which may comprise a silicon dioxide glass wafer or a silicon-germaniumwafer, instead of a silicon wafer, with circumferential slot segments todefine a planar cylindrical resonator with embedded electrostaticsensors and actuators. Preferably, the silicon dioxide glass wafercomprises fused quartz (also known as vitreous silica, fused silica orsilica glass) or PYREX (also known as borosilicate glass). A novelpost-fabrication process yields a high quality (10,000,000 Q)axisymmetric, mesoscale, electrically conductive, mechanical resonatorwith navigation grade performance. The structure is micromachined withDRIE (deep reactive ion etching), in the same fashion as thesilicon-based disc resonator gyroscope described in the parent patentapplications referenced above, but with an etcher designed for quartzand/or silicon-germanium.

Integral capacitive electrodes can be formed within these slots from theoriginal resonator during the through etch process. This can beaccomplished by first bonding the unmachined resonator disc to a basewafer that is specially prepared with circumferential bonding pillarsegments to support the stationary electrodes and central resonator. Thepillar heights may be defined by dry RIE (reactive ion etching) or wetchemical etching, and a number of bonding techniques (such as thermalcompression bonding, eutectic bonding, fusion bonding, anodic bonding,diffusion bonding, optical contact (Van der Waals force) bonding, orsolder bonding) can be used to bond the resonator to the support pillarsbefore the resonator and its electrodes are photolithographicallymachined using DRIE. The dense wiring can be photographed onto thebaseplate before resonator bonding or can reside on a third wafer whichis bonded to the baseplate/resonator pair at a latter time to formelectrical connections to the resonator and electrodes. A conductivefilm is deposited via CVD (chemical vapor deposition), ALD (atomic layerdeposition), or another substantially conformal deposition process (suchas sputtering or evaporation) onto the machined resonator and electrodesand selectively etched to render them electrically conductive withoutotherwise effecting electrical connections to the electrodes. Thesilicon-germanium wafer may be doped and/or plated as necessary. Thewiring can then be wirebonded outside the device to a wiringinterconnect grid or interconnected to a readout electronics wafer viavertical pins etched into the resonator.

FIGS. 3A-3C depicts various stages of an exemplary manufacturing processfor the invention. FIG. 3A shows a sequential development of thebaseplate for the resonator gyroscope (e.g., from the top to bottomelement). The process begins with fused quartz or PYREX orsilicon-germanium wafer 300 as shown in the first or top element of FIG.3A. The wafer 300 is first etched to produce electrode pillars 302 aswell as a central resonator support pillar 304, such as for a singlecentral support as shown in the second element of FIG. 3B. The etchingprocess can be an RIE process (such as CF4₄/O₂ plasma RIE) or a wetetching process, such as BOE (buffered oxide etch) or HF (hydrogenfluoride) etching. Photoresist can be patterned via photolithography andused as a mask, or masks made from other materials may be used (such asmetals, or polysilicon). The third element of FIG. 3A shows a dielectriclayer 306 that may be applied over the etched wafer 300 if that wafer iselectrically conductive (such as SiGe). The dielectric is preferablysilicon dioxide, but other dielectrics (such as silicon nitride) may beused as well. This layer 306 can be applied by growing a wet thermaloxide or by another dielectric deposition method such as PECVD (plasmaenhanced CVD), LPCVD (low pressure CVD), evaporation, or sputtering. Theoxide layer 306 can then be etched, e.g., with BOE or RIEA metalizationlayer is then applied to form bonding pads 308, 310 on each of thepillars 302, 304, respectively, as shown in the fourth or bottom elementof FIG. 3A. Application of the metalization layer can be accomplished bymask lithography, depositing the mask (e.g., AZ 5214 at 2000 RPM for 20seconds). The metal, e.g., 100 Angstroms Ti, 200 Angstroms Pt and 3500Angstroms Au, is then deposited and the mask is lifted off to yieldmetal bonding pads 308, 310 only on the surfaces of the pillars 302,304.

Application of the metalization layer for the bonding pads can alsoinclude patterning of the electrical wiring from the electrodesphotographed onto the baseplate, wirebonded outside the device to awiring interconnect grid on a ceramic. Alternately, in further novelembodiments discussed hereafter, the electrical wiring can bealternately developed into an integral vacuum housing producedsimultaneously with the resonator.

FIG. 3B shows a sequential development of the resonator wafer for thegyroscope (e.g., from the top to bottom element). The first or topelement of FIG. 3B shows the uniform thickness fused quartz or PYREX orsilicon-germanium wafer 312, used to form the resonator. The wafer 312can first have the back side processed to produce alignment marks withmask lithography applying a resist. The alignment marks can be producethrough a RIE process using CF₄ and O₂ until a relief is clearly visible(approximately 5 to 10 minutes). Alternately, an STS (Surface TechnologySystems) process for approximately 1 minute can also be used. Afterremoving the resist, metalization lithography used to apply a mask tothe front side of the wafer 312 to produce bonding pads 314, 316, asshown in the second or bottom element of FIG. 3B. The metal, e.g., 30Angstroms Cr and 3500 Angstroms Au or 100 Angstroms Ti, 200 Angstroms Ptand 3500 Angstroms Au, is applied and the mask is lifted off to revealthe bonding pads 314, 316.

FIG. 3C shows integration of the resonator and baseplate wafers andformation of the functional resonator for the gyroscope (e.g., from thetop to bottom element). The preprocessed baseplate wafer 300 andresonator wafer 312 are bonded together, as shown in the first or topelement of FIG. 3C, after aligning the two wafers 300, 312 toapproximately 1 micron. Bonding fuses the metal bonding pads (theelectrode pads 308, 310 as well as the central support bonding pads 314and 316) to form single bonded metal joints 318 and can be performed atapproximately 400° C. and 5000 N. Next, the complete resonator 330 andelectrodes 332A, 332B (generally referenced as 332) are simultaneouslyformed directly from the bonded structure by through etching, as shownin the second or bottom element of FIG. 3C. The through etching processcan be performed using DRIE, such as a suitable STS process with aphotolithographically defined mask, e.g., an AZ 5740 mask, approximately6 to 8 microns thick, or with a patterned metal mask (such as Cr, Ni,Al, or Pt). The mask can be made as thin as possible for throughetching. The resonator wafer 312 is then etched through the mask patternto simultaneously produce the resonator 330 as well as the separateelectrodes 332A, 332B from the original wafer 312. See also FIGS. 2A-2C.Note that single electrodes 332 can be formed by through etching,forming passages 322, 324, to isolate a section of the resonator wafer312 attached to a bonded joint 318. In addition, as discussed above withrespect to FIG. 1B, electrodes can also be divided into multipleseparate elements. For example, through etching an additional passage326 separates the electrode 332 into two isolated electrode elements332A, 332B. In this case, the passage 326 must penetrate the metalbonded joint 318 to isolate the separate electrode elements 332A, 332B.To achieve this, the metal pads 308 and 314 must be split to accommodatea gap that passage 326 will be aligned with when the through-etch takesplace. At the conclusion of the through etching process, the resonator330 structure is only supported at the central resonator support pillar304. In the case where the resonator material is electrically insulating(such as the preferred fused silica material), the resonator andelectrode surfaces must be rendered conductive by depositing a thinconductive layer onto them. This is preferably accomplished by CVD orALD of very thin conductive material, preferably a metal (Al, Cr, Ni,Pt, or Au), onto the resonator surface and selectively etching thematerial to remove it from the areas (such as the bottom of passage 326)where it may form undesirable shorts between separate electrodes, e.g.,332A and 332B. This is accomplished by a directional etching processsuch as ion milling or DRIE.

FIG. 3D shows an exemplary resonator 330 with a quarter cutaway toreveal the embedded electrodes 332. A dust ring 334 is also shown thatcan be etched along with the resonator 330. Intermittent gaps 336 in thedust ring support pillar can be made to accommodate metal traces to theelectrodes 332 to operate the gyro.

A variety of fabrication process flows are possible to achieve thestructure shown in FIG. 3D. A number of possible process flows aresummarized in FIGS. 3E and 3F. The selection of the best process flow isdriven first by the choice of resonator material, and subsequently byprocess optimization for device yield and fabrication cost given theavailable equipment limitations and achievable tolerances. For example,aligned bonding is known to be a challenging step using readilyavailable bonder-aligners, and so, at the present time, a process flowthat avoids this step may be desirable. When bonding tools withsubstantially higher alignment precision and repeatability becomereadily available, a simpler process requiring the least number ofprocess steps and thus minimizing device cost may become optimal.

The exemplary planar resonator gyroscope embodiments presented hereincan be integrated with typical vacuum packaging and electronics in amanner similar to previous gyroscopes. However, the internal ceramicsubstrate wiring bonded to the gyroscope can be changed to match the newand old designs to existing packages.

FIG. 3G shows an exemplary gyroscope in a typical packaging assembly.Metal traces 338 from the electrodes 332 of the resonator 330. The dustring 334 with intermittent gaps 336 allows passage of the metal traces338 on the baseplate wafer 300 to the electrodes 332. The metal traces338 lead to vertical connect pins 340 which pass through the baseplatewafer 300 (providing a vacuum seal). In the exemplary architectureshown, the vertical connect pins 340 are disposed in the corners of thesquare baseplate wafer 300. A vacuum cavity wall 342 surrounds theentire assembly. The vacuum cavity wall 342 can be applied as a part ofa conventional housing covering the resonator 330 and bonded to thebaseplate wafer 300. Alternately, in further embodiments discussedhereafter, an vacuum cavity wall 342 can be produced simultaneously withthe resonator.

FIG. 4 is a flowchart of an exemplary method 400 of fabricating aninertial sensor according to the present invention. Block 402 representsetching a baseplate, Block 404 represents bonding a thermallynon-conductive wafer, such as a silicon dioxide glass wafer (a silicaglass wafer or a borosilicate glass wafer) or a silicon-germanium wafer,to the etched baseplate, Block 406 represents through-etching thethermally non-conductive wafer to form a mesoscaled disc resonator,Block 408 represents depositing a thin conductive film on thethrough-etched thermally non-conductive wafer, Block 410 representsselectively etching the thin conductive film to render thethrough-etched thermally non-conductive wafer electrically conductivewithout otherwise effecting electrical interconnect wiring thereon,thereby fabricating the inertial sensor.

The specifics of the above method are described in more detail below forboth electrically non-conductive and conductive resonators.

For example, for a fused silica glass mesoscale gyroscope, thefabrication process of FIG. 4 for a electrically non-conductiveresonator where the baseplate has no electrical wiring (nominally, athree-wafer structure) comprises the following. First, there isbaseplate/resonator fabrication by pillar photolithography, pillar RIE,fusion bonding, resonator metal photolithography, metal evaporation,liftoff, resonator STS photolithography, resonator STS, resist removalby O₂ RIE, conductive thin film deposition, and conductive thin filmetch. Second, there is capping wafer fabrication by pillarphotolithography, pillar RIE, bottom metal evaporation, bottom metalphotolithography, bottom metal etch, PECVD oxide deposition, PECVD oxidelithography, PECVD oxide RIE, top metal lithography, top metaldeposition, liftoff, bonding metal lithography, bonding metaldeposition, and liftoff. Third, there is fabrication of the three-waferstack for the disc resonator gyroscope by bonding and dicing.

In another example, for a fused silica glass mesoscale gyroscope, thefabrication process of FIG. 4 for a electrically non-conductiveresonator where the baseplate has electrical wiring (nominally, atwo-wafer structure) comprises the following. First, there is baseplatewafer fabrication by pillar photolithography, pillar RIE, bottom metalevaporation, bottom metal photolithography, bottom metal etch, PECVDoxide deposition, PECVD oxide lithography, PECVD oxide RIE, top metallithography, top metal deposition, and liftoff. Second, there isfabrication of the resonator by resonator metal photolithography, metalevaporation, and liftoff. Third, there is fabrication of thebaseplate/resonator combination by bonding, resonator STSphotolithography, resonator STS, resist removal by O₂ RIE, deposition ofthe thin conductive layer by CVD or ALD, and selective etch of the thinconductive layer.

4.0 Experimental Results

The following tables describe various mesoscale disc resonator gyroscopedesigns using fused quartz and silicon with the same masks, and therebyillustrate the benefits of micromachined mesoscale resonators andparticularly the superior intrinsic thermoelastic quality factor (QTED)of micromachined fused quartz. A definition of thermoelastic damping(see, e.g., T.V. Roszhart, “The effect of thermoelastic internalfriction on the Q of micromachined silicon resonators,” in IEEE SolidState Sensor and Actuator Workshop, Hilton Head, SC, 6 4-7, 1990, pp.489-494, which is incorporated by reference herein), as discovered byZener for simple beams, intrinsic material damping Q₀ and amplificationfactor Γ are first defined as follows:

-   -   Q_(TED)=ΓQ₀, thermoelastic damping        ${Q_{o} = \frac{2C_{v}}{E\quad\alpha^{2}T_{o}}},$    -   intrinsic material quality        ${\Gamma = {\left( {x + \frac{1}{x}} \right)/2}},$    -   thermoelastic tuning factor x=f/f₀        ${f_{o} = \frac{\pi\quad K}{2C_{v}b^{2}}},$    -   Debye frequency or inverse thermal relaxation period    -   f=beam vibration frequency    -   C_(V)=specific heat capacity    -   K=thermal conductivity    -   b=beam width    -   E=Young's Modulus    -   α=coefficient of thermal expansion    -   T₀=nominal beam temperature

Isothermal vibration and high QTED results when Γ<<1, as withconventional microscale MEMS or alternatively, adiabatic vibration andhigh QTED can result if Γ>>1, as has been achieved with the planarmesogyroscopes described herein. TABLE 1 Comparison of IntrinsicMaterial Quality Crystalline Crystalline Fused Silicon Diamond QuartzQuartz Minimum Thermoelastic Quality 10,000 16,500 795  855,000 ThermalConductivity, K [J/(K * m{circumflex over ( )}³)]   159   2000 10 1.7Specific Heat Capacity, C_(v [J/(K * s * m)]) 1.636e6 1.81e6   1.74e6  1.54e6   Young's Modulus, E [N/m{circumflex over ( )}²]   160e9   113478 75 Thermal Expansion Coefficient, α    2.6e−6  0.8e−6 13.7e−6   4e−7

The surprisingly high intrinsic material quality of fused quartz vs.traditional MEMS materials such as silicon used for micromachinedcapacitive inertial sensors or crystalline quartz used for piezoelectrictuning forks is seen to be a result of its combined low thermalconductivity and low coefficient of thermal expansion. The discresonator gyroscope micromachined from fused quartz at mesoscale andmade electrically conductive for capacitive sensing can now fullyexploit substantially thermally non-conductive materials such as fusedquartz that are not piezoelectrically active. TABLE 2 DRG Design StudySummary DISC Ring Frequen- FoM = DIA. width, cy, fr 360fr/ Material MMum Hz Q_TED (2Qk) deg/s Crystal Silicon 16 170 27,355 26,700 234 CrystalSilicon 8 18.5 12,400 154,000 18.3 Crystal Silicon 1.6 4 61,232 780,00017.9 Crystal Silicon 2.0 5 49,265 620,000 18.1 Crystal Silicon 2.0 2.523,126 5,285,000 1.0 Fused Quartz 16 170 19,265 137,000,000 0.0316 FusedQuartz 8 18.5 8,753 1,085,000 1.84 Fused Quartz 1.6 4 42,360 1,245,0007.72 Fused Quartz 2.0 5 34,314 1,067,000 7.32 Fused Quartz 2.0 2.514,503 8,092,000 0.4

For example, compare the mesoscale fused quartz design example in Table2 with a 16 mm resonator at Q=137,000,000 to the mesoscale silicondesign with a 16 mm resonator at Q=26,500. This represents a remarkable5300× improvement in quality and comparable improvement in overallgyroscope mechanical figure of merit (FoM) of a mesoscale disc resonatorgyroscope micromachined from substantially thermally non-conductivefused silica vs. conventional silicon . The advantages of this approachbeyond its exceptional mechanical quality are further revealed when itis recognized that the 170 um ring width of the mesoscale 16 mm diameterfused quartz design is 70× the 2.5 um ring width of the optimum 2 mmdiameter microscale for conventional silicon. For fixed etch error of0.1 um this leads to 70× improvement in relative precision of itsmicromachined symmetry, tuning performance and inherent drift. At thesame time, the remarkable thermoelastic properties of fused quartz alsomake it more advantageous than silicon at microscale even though itsvibration is not as isothermal and its amplification factor

is lower. Various other materials, scales and geometry can be consideredusing finite element analysis; however, a mesoscale planar resonatormicromachined from substantially thermally nonconductive material thatcan be used for capacitive operation is the key to high performance.

5.0 Alternate Isolated Planar Resonator Gyroscope

An exemplary centrally supported planar resonator having concentriccircumferential slots with internal electrodes to produce substantiallyin-plane vibration is described above. However, it is important to notethat other planar resonator patterns are also possible using theprinciples and procedures described.

FIG. 5 illustrates an alternate isolated planar resonator gyroscopeembodiment comprising four masses vibrating in plane. In thisembodiment, the resonator 500 comprises a plate including foursubresonator mass elements 502A-502D (generally referenced as 502) eachoccupying a separate pane of a supporting frame 504. The frame isattached to a baseplate (not shown) at a central support 506. Eachsubresonator mass element 502A-502D, is attached to the frame 504 by oneor more support flexures 508. In the exemplary resonator 500, foursupport flexures 508 each having a meander line shape are attached toeach mass element 502A-502D, one attached to each of the four sides ofthe element 502. Each support flexure 508 is attached to two corners ofthe mass element 502 at its ends and attached to an adjacent side of thepane of the support frame 504 at its middle. Each mass element 502A-502Dincludes eight groups of linear electrodes 510 (each electrode includingtwo elements) arranged in a pattern of increasing length from a centralpoint of the mass element 502. Each subresonator mass element 502A-502Dhas a pair of simple degenerate in-plane vibration modes to yield twodegenerate in-plane system modes involving symmetric motion of all fourelements 502A-502D, suitable for Coriolis sensing. Note that despite thesignificant differences in the architecture between this embodiment andthat of FIGS. 1A-1B, both still utilize planar mechanical resonators forsubstantially in-plane isolated and degenerate modes for Coriolissensing with internal excitation and sensing electrodes.

There are some key advantages of this alternate in-plane designembodiment over other out-of-plane gyros. For example, this embodimentincludes a central support 506 bond that carries no vibratory loads,virtually eliminating any possible friction. In addition, simultaneousphotolithographic machining of the resonator and electrodes can beachieved via the slots. Further, with this embodiment, diametralelectrode capacitances can be summed to eliminate vibrationrectification and axial vibration does not change capacitance to a firstorder. The modal symmetry is largely determined by photolithographicsymmetry, not wafer thickness as with gyros employing out-of-planevibration. Also, this embodiment employs isolation and optimization ofthe sense capacitance (e.g., the outer slots of each element) and thedrive capacitance (e.g., the inner slots of each element) and provides ageometrically scalable design to smaller/larger diameters andthinner/thicker wafers. This embodiment can also be entirely defined byslots of the same width for machining uniformity and symmetry. Finally,with this embodiment four-fold symmetry is well suited for the mostcommonly available (100) crystal orientation SiGe wafers and an idealangular gain approaches one.

Wiring can be photographed onto the baseplate and wirebonded outside thedevice to a wiring interconnect grid as discussed above. However,implementation of this alternate embodiment can require many electrodesand interconnect wiring. As discussed below, the electrical wiring forthis embodiment can also be alternately developed into an integralvacuum housing produced simultaneously with the resonator. Such animplementation is detailed hereafter.

There is also a potential interaction with degenerate pairs of othersystem modes very close in frequency. However, these can be ignored ifnot coupled. In addition, the central support and frame compliance canbe modified to shift any coupled modes away in frequency.

This embodiment can also employ final mechanical trimming with a laseror focused ion beam (FIB) to achieve symmetric, fully tuned, degeneratemode performance over thermal and vibration environments. This techniqueis described in U.S. Pat. No. 6,698,287, which is incorporated byreference herein. It is also noted that the isolation of the degeneratemodes used in present embodiments of the invention can also be trimmedelectrostatically, as with the embodiments discussed above and otherout-of-plane gyro designs.

It is recognized that other low thermal conductivity materials with lowthermal expansion coefficient, e.g., ZeroDur®, may also be suitable fora micromachined mesogyroscope and that there are other means for makingsuch desirable materials conductive for mesogyro resonator applications,such as metal chemical vapor deposition, metal plating, atomic metallayer deposition, and surface doping.

This alternate embodiment can also be packaged using conventionaltechniques. However, as discussed hereafter, the resonator can also beintegrated into a novel integrated vacuum housing formed by resonatorbaseplate, case wall and readout electronics.

6.0 Conclusion

The foregoing description of the preferred embodiment of the inventionhas been presented for the purposes of illustration and description. Itis not intended to be exhaustive or to limit the invention to theprecise form disclosed. Many modifications and variations are possiblein light of the above teaching. It is intended that the scope of theinvention be limited not by this detailed description, but rather by theclaims appended hereto. The above specification, examples and dataprovide a complete description of the manufacture and use of theinvention. Since many embodiments of the invention can be made withoutdeparting from the scope of the invention, the invention resides in theclaims hereinafter appended.

1. A method of fabricating a mesoscaled resonator for an inertialsensor, comprising: etching a baseplate; bonding a substantiallythermally non-conductive wafer to the etched baseplate; andthrough-etching the substantially thermally non-conductive wafer to forma mesoscaled resonator with capacitive electrodes.
 2. The method ofclaim 1, wherein the wafer is a silicon-germanium wafer.
 3. The methodof claim 1, wherein the wafer is a silicon dioxide glass wafer, and themethod further comprises: depositing a thin conductive film on thethrough-etched wafer; and selectively etching the thin conductive filmto render the through-etched wafer electrically conductive withoutotherwise effecting electrical interconnect wiring thereon.
 4. Themethod of claim 3, wherein the silicon dioxide glass wafer is a silicaglass wafer or a borosilicate glass wafer.
 5. The method of claim 1,wherein the through-etching is performed using deep reactive ionetching.
 6. The method of claim 1, wherein the through-etching of thewafer forms a case wall for the inertial sensor.
 7. A mesoscaledresonator for an inertial sensor fabricated using the method of claim 1.